We consider the localization of a mobile millimeter-wave client in a large indoor environment using multilayer perceptron neural networks (NNs). Instead of training and deploying a single deep model, we proceed by choosing among multiple tiny NNs trained in a self-supervised manner. The main challenge then becomes to determine and switch to the best NN among the available ones, as an incorrect NN will fail to localize the client. In order to upkeep the localization accuracy, we propose two switching schemes: one based on a Kalman filter, and one based on the statistical distribution of the training data. We analyze the proposed schemes via simulations, showing that our approach outperforms both geometric localization schemes and the use of a single NN.